How would I solve a system of equations that involve logs?

Question

I'm encountering a problem with solving this system where I can't quite figure out what direction I should be going to start this off. Here are the equations.

(logx)(logy) - 3log5y - log8x = -4

(logy)(logz) - 4log5y - log 16z = 4

(logz)(logx) - 4log8x -3log625z = -18

Answer 1

Hopefully this is a more helpful answer:

first equation:

logx logy - 3 log 5 - 3 log y - log 8 - log x = -4 <--- property of logs: log(AB) = logA + logB;

BUT, there is -3 multiplied in front of 2nd term and

-1 multiplied in front of 3rd term

log x log y - logx = log8 - 4 + 3log5

logx( log y - 1) = log8 - 4 + 3log5

log y = { (log 8 - 4 + 3 log 5)/ (log x) } + 1

= (logx + k)/logx where k = log 8 - 4 +3 log 5

So now we have log y isolated in terms of log x

You can substitute that into the second equation, and then you will have 2 equations in terms

of log x and log z, that is, reduced to a 2 by 2.

Perhaps you can rewrite the second and third equations in a similar way to make it a little easier.

GOOD LUCK!